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Optimal asymptotic quadratic error of density estimators for strong mixing or chaotic data

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  • Bosq, Denis
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    Abstract

    Under mild mixing conditions, we show that the kernel density estimator has exactly the same asymptotic quadratic error as in the i.i.d. case. Curiously, that result remains almost valid if the data are chaotic.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-448R1X6-D/2/5589964f300340ef4a70b2105d8f0e9e
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 22 (1995)
    Issue (Month): 4 (March)
    Pages: 339-347

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    Handle: RePEc:eee:stapro:v:22:y:1995:i:4:p:339-347

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    Related research

    Keywords: Density estimation Optimality Mixing Chaos;

    References

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    1. Vieu, Philippe, 1991. "Quadratic errors for nonparametric estimates under dependence," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 324-347, November.
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    Cited by:
    1. D. Blanke & D. Bosq & D. Guégan, 2003. "Modelization and Nonparametric Estimation for Dynamical Systems with Noise," Statistical Inference for Stochastic Processes, Springer, vol. 6(3), pages 267-290, October.
    2. Biau, Gérard, 2002. "Optimal asymptotic quadratic errors of density estimators on random fields," Statistics & Probability Letters, Elsevier, vol. 60(3), pages 297-307, December.
    3. N. Hosseinioun & H. Doosti & H. Nirumand, 2012. "Nonparametric estimation of the derivatives of a density by the method of wavelet for mixing sequences," Statistical Papers, Springer, vol. 53(1), pages 195-203, February.

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